Date: 27 October 2021 | Speaker: Oscar Finnegan
Group theory is the mathematical study of symmetry and is ubiquitous across the entire spectrum of mathematics. Simple groups play a similar role in group theory to prime numbers in the integers, they form a kind of “building block” that every group is made from. Classifying finite simple groups was a titanic effort undertaken in the 20th century, whose completion took hundreds of authors, over 10,000 pages worth of proof, and forms one of the greatest mathematical achievements of the last hundred years.
I will give a brief overview of group theory and define simple groups, in order to state the classification theorem and give a short history of the proof. Out of the classification theorem arises the Monster, the largest sporadic finite simple group, whose study I will also discuss.
